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Statistics

 Decile
 compute deciles

 Calling Sequence Decile(A, d, ds_options) Decile(M, d, ds_options) Decile(X, d, rv_options)

Parameters

 A - M - X - algebraic; random variable or distribution d - algebraic expression or list of algebraic expressions; deciles ds_options - (optional) equation(s) of the form option=value where option is one of ignore, method, or weights; specify options for computing the decile of a data set rv_options - (optional) equation of the form numeric=value; specifies options for computing the decile of a random variable

Description

 • The Decile function computes the specified decile of the specified random variable or data set.
 • The first parameter can be a data set (e.g., a Vector), a Matrix data set, a distribution (see Statistics[Distribution]), a random variable, or an algebraic expression involving random variables (see Statistics[RandomVariable]).
 • The second parameter d is a decile or list of deciles.

Options

 For a description of the available options, see the Statistics[Quantile] help page. Calling Decile with decile $d$ is equivalent to calling Quantile with probability $0.1d$.

Examples

 > $\mathrm{with}\left(\mathrm{Statistics}\right):$

Compute a decile of the Weibull distribution with parameters a and b.

 > $\mathrm{Decile}\left(\mathrm{Weibull}\left(a,b\right),3\right)$
 ${a}{}{{\mathrm{ln}}{}\left(\frac{{10}}{{7}}\right)}^{\frac{{1}}{{b}}}$ (1)

Use numeric parameters.

 > $\mathrm{Decile}\left(\mathrm{Weibull}\left(3,5\right),3\right)$
 ${3}{}{{\mathrm{ln}}{}\left(\frac{{10}}{{7}}\right)}^{{1}}{{5}}}$ (2)
 > $\mathrm{Decile}\left(\mathrm{Weibull}\left(3,5\right),3,\mathrm{numeric}\right)$
 ${2.44104494075064}$ (3)
 > $\mathrm{StandardError}\left[{10}^{5}\right]\left(\mathrm{Decile},\mathrm{Weibull}\left(3,5\right),3,\mathrm{numeric}\right)$
 ${0.00283364066608145}$ (4)

Generate a random sample of size 100000 drawn from the above distribution and compute the sample decile.

 > $A≔\mathrm{Sample}\left(\mathrm{Weibull}\left(3,5\right),{10}^{5}\right):$
 > $\mathrm{Decile}\left(A,3\right)$
 ${2.44048423337317}$ (5)
 > $\mathrm{StandardError}\left(\mathrm{Decile},A,3\right)$
 ${0.00259397498616096428}$ (6)

Consider the following Matrix data set.

 > $M≔\mathrm{Matrix}\left(\left[\left[3,1130,114694\right],\left[4,1527,127368\right],\left[3,907,88464\right],\left[2,878,96484\right],\left[4,995,128007\right]\right]\right)$
 ${M}{≔}\left[\begin{array}{ccc}{3}& {1130}& {114694}\\ {4}& {1527}& {127368}\\ {3}& {907}& {88464}\\ {2}& {878}& {96484}\\ {4}& {995}& {128007}\end{array}\right]$ (7)

We compute the sixth decile for each column.

 > $\mathrm{Decile}\left(M,6\right)$
 $\left[\begin{array}{ccc}{3.53333333333333}& {1067.}& {121453.466666667}\end{array}\right]$ (8)

References

 Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.

Compatibility

 • The Statistics[Decile] command was updated in Maple 16.
 • The M parameter was updated in Maple 16.